Adaptive Virtual Fixture Based on Learning Trajectory Distribution for Comanipulation Tasks

Virtual fixture is a powerful tool to improve safety and efficiency for co-manipulation tasks. However, traditional virtual fixtures with constant stiffness are inadequate for scenarios where robots need to leave the constraints to perform tasks. To address this, we propose an adaptive virtual fixture based on the motion refinement tube, which dynamically adjusts the guiding force according to the distribution of trajectories. To prevent tube deformation in the Cartesian space due to the neglect of off-diagonal elements of covariance matrices, the refinement tube radii and nonlinear stiffness terms are computed in local coordinate systems based on the decomposed covariance matrix. An energy-tank-based passivity controller is designed to ensure system stability when employing the virtual fixture with state-dependent stiffness terms. In the validation tests with 18 participants, the proposed method showed improvements in task efficiency (18.69% increase) and collision avoidance (97.87% reduction) for a typical pick-and-place task with scattered materials. It also provided better subjective experiences of the users than traditional virtual fixtures. Meanwhile, compared with the method that neglects off-diagonal elements of the covariance matrix, the proposed method exhibited a 4.28% efficiency improvement and a 40.42% decrease in collision occurrences.